Many signal classifiers must be optimized with few training samples, which requires to build structured signal representations. This project first considers unsupervised problems where the representation is constructed without knowing the classification task and any class label. A goal of this research is to show that such representations can be constructed with joint multiresolution representations of signals and deformation operators, which provide local invariants that are well adapted to classification problems. The Gestalt school of psychophysics has demonstrated that grouping patterns has a major role for visual and auditory recognition. Grouping operators will be revisited from a harmonic analysis point of view, showing that such operators can indeed identify deformations and build invariant representations. A second goal is to develop classification algorithms in a supervised context, which take advantage of these local invariant representations, and which can scale to large size recognition problems. A last aspect of this project is to relate this mathematical construction to the study of the V1 and subsequent areas in the visual cortex, and develop new mathematical models of complex cells that will be evaluated with fMRI recordings.
The project is organized in four parts. The first part aims at defining a multiresolution framework which integrates signal and deformation operator representations. We intend to derive signal representations that are ``locally'' invariant to specific classes of deformations that belong to Lie groups. The second part concentrates first on unsupervised estimation of grouping templates to construct these multiresolution invariants. These tools will then be applied to classification algorithms that will be tested on classification data bases. The third part is devoted to the statistical modeling of multiscale deformations in a supervised framework, to improve classification results. The last part concerns the study of complex cell models in the visual cortex V1 and the ventral visual pathway, derived from this research and new methodological tools in fMRI.
CMAP ECOLE POLYTECHNIQUE
ANR grant: 219 996 euros
Project ID: ANR-10-BLAN-0126
Monsieur Stéphane MALLAT (ECOLE POLYTECHNIQUE)
The project coordinator is the author of this abstract and is therefore responsible for the content of the summary. The ANR disclaims all responsibility in connection with its content.